


li 



Hollinger Corp. 
P H8.5 



— PROPERTY OF 
THE AMERICAN ASSOCIATION 
F0R THE ADVANCEMENT OE SCIENCE. 



S03 i M 






WATERS WITHIN THE EARTH 



LAWS OF RAINFLOW 



BY 

W. S. AXJCHINCLOSS, C.E. 

author of " link and valve motions "—{German Edition, "Scheiber-und Coulissensteurungen ") 

ALSO OF "NINETY DAYS IN THE TROPICS" 

FELLOW AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE 
MEMBER INSTITUTO POLYTECHNICO BRAZILIERO 



PHILADELPHIA 



Copyright 

W. S. Auchinoloss 

1897 




JAN 1 8 1936 



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C^^lSC?^ 




41' Vr«..-»^EJ 



JAN 1 8 1936 




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.M 



WATERS WITHIN THE EARTH. 



An abundant supply of fresh water is so essential to all the 
activities of life, that everywhere the question of rainfall is regarded 
with the keenest interest, and stations have been established through- 
out the world for keeping accurate records of the times and amounts 
of downpour. These observations, however, go no further than 
the surface of the ground. They tell us nothing about the subse- 
quent history of the water as it journeys onward through the dark 
recesses of the earth ! How much of it is taken up by evaporation ? 
How much is needed to satisfy the demands of plant-life? Much 
less do they give the faintest idea of what quantity reappears in 
lake or stream after months of unseen flow ? 

Our research has the twofold object of supplying the missing 
history and developing the laws of subterranean flow, or, more con- 
cisely, rainflow. The standard for measure and comparison will 
be the household well, because it is fouud in every country and 
affords a ready access for underground study. 

Let us trace the progress of a summer storm ! — 

The first drops that fall simply moisten the ground. Gradually 
the surface becomes saturated, after which water can no longer 
enter the soil as fast as the rain falls. The excess, therefore, must 
glide away over the surface to the lowlands. When the storm ceases 
a portion of the water will evaporate, but a larger portion will be 
taken up by vegetation. It is generally conceded among agricul- 
tural authorities that grasses and herbs require for perfect growth a 
daily supply of water equal to their own weight Possessed of so 
great capacity, we can readily understand how the midsummer 
demand seizes all that escapes evaporation, and for the time being 
stops all further descent of the water. With the disappearance of 
vegetation during the winter months this demand ceases and the 

(3) 



water continues its descent as rapidly as the nature of the soil per- 
mits. Finally, it falls into what may properly be called the great 
subterranean lake, or, more concisely, the sublake. This body of 
diffused water underlies the earth's surface and is almost coextensive 
with its area. Its universal character is evidenced by the fact that 
wherever a well is sunk to a sufficient depth one is sure to find the 
sublake, and its water will fill the cavity only to the level of the sub- 
lake. We have described it as a body of diffused water, because its 
globules fill the interstices of the soil, sand, or disintegrated rock 
among whose particles it exists. Furthermore, it fills all fissures 
and openings in subjacent rock to which it has access. Most rocks 
are wholly impervious to water, but their extensive fissures store it 
in vast quantities. When, therefore, a well pierces one of these 
fissures an abundant supply is fully guaranteed. .Evidently in 
sinking a well through solid rock the result is always a matter of 
chance, and depends upon whether the drill encounters a fissure 
large enough to give the needed supply without going to some extra- 
ordinary depth. Occasionally a hillside fissure is not perfectly 
enclosed, but has a minute opening at the surface of the ground. 
In such case the water bubbles forth as a refreshing spring. Artesian 
wells count their depth by hundreds of feet, and finally pierce water- 
bearing strata' whose surface outcrop is likely to be found many 
miles distant. These storage strata are filled with water of the great 
sublake. When the lake surface stands at a greater elevation than 
the mouth of the well, the discharge takes place under pressure and 
the water rises like a fountain. 

In making a comparison between the sublake and lakes found on 
the earth's surface, we observe : 

1st. The sublake is not affected by storms. 

2c?. It has no tide. 

2>d. Its surface is never frozen. 

4th. It lacks mobility. 
These characteristics are principally due to the mass of soil over- 
lying the sublake, but the last feature is developed by the resistance 
of the particles around which the water is obliged to work its way. 
Hence the surface of the sublake is undulating in a hilly country. 
If all hills were composed of coarse gravel, all rainfalls entering the 



earth would quickly find a common level. It is only due to the 
close texture of the soil that the water is held back upon the hillsides, 
and so little is lost, in the intervals between storms, by percolation, 
that it continues in a banked-up state from year to year, ever part- 
ing with what it receives, and ever receiving fresh supplies from 
above. 

Fig. 1. 




Wells that are dug in hillsides, as in Fig. 1, reveal the surface of 
the sublake far above the level of the brook in the adjoining valley, 
yet the brook owes its own permanence to the sublake, whose waters 
for many months descending through subterranean passages ulti- 
mately reach the level of the brook and maintain its flow in times 
of drought. For our study a hilltop well is preferable, and its lining 
should exclude all surface water for a depth of at least 10 feet below 
the curb. 

Influx depends upon the presence or absence of rainfall, clouds, 
and fog, the activity of vegetation, and at times upon the frozen 
condition of the soil. 

Efflux is the overflow of the sublake, and occurs at a depth far 
below the reach of local causes, where earth and water are practi- 
cally of one temperature throughout the entire year, where ice is 



unknown, and the earth's covering of snow exerts no appreciable 
influence on the flow. In a word, efflux goes on throughout the 
entire year, holding its even course, and for a given locality ever 
flowing at one continuous speed. 

As the sublake is the resultant of influx and efflux, its surface 
rises or falls as one or the other gains the mastery. 

A simple experiment with a dish, a huge sponge, and a pitcher of 
water will give a clear idea of the principle of influx. The dish 
represents the impervious clay or bed-rock beneath the soil which 
entirely stops the descent of the water. The sponge represents the 
surface soil that is open and porous, or the disintegrated rock. The 
pitcher of water symbolizes the annual rainfall. If water is poured 
over the sponge its porous cells will for some time take up all we 
give and the dish will remain dry. But continuing to pour, the 
cells will at length become saturated, and further additions cannot 
be made, because the surplus will simply pass through the sponge 
and accumulate in the dish below. The accumulation in the lower 
part of the sponge is a true counterpart of the sublake. 

We learn from this experiment that no water can reach the sublake 
unless complete saturation of the soil first takes place. That the 
rapidity of flow depends on the texture of the soil through which 
the water percolates. Also that its efflux in a given time is practi- 
cally constant, because the lay of the land naturally limits the border 
of the sublake. This feature of constancy is a most important 
factor in the study of the fluctuations, — in fact, a key to the situ- 
ation, for it renders intelligible movements that otherwise would 
seem obscure. 

The Sublake. 

The changes that are perpetually taking place iu climatic condi- 
tions give little rest to the sublake. They in fact develop both 
Annual and Periodic fluctuations and cause the waters to rise and 
ebb with tide-like flow. 

Annual fluctuations showing a range of 63 inches are graphi- 
cally portrayed in Fig. 2, which gives sectional views of a single 
well, and shows the relative height of water for five different months. 



The heights for intermediate times are expressed by the curved line 
joining these surfaces. 



Fig. 2. 




Fig. 3. 




Periodic fluctuations showing a range of 20 feet are illustrated 
by Fig. 3. It should be noted that the maximum and minimum 
points are separated by years. In reaching these points the normal 



level may be crossed as often as twice in one year ; still years occur 
in which the surface fails to pass the normal once. 

During the past ten years a careful record has been kept of the 
water-level in Hill Crest well, Bryn Mawr, Pa. The readings 
have been tabulated plus (+) when influx prevailed, minus ( — ) 
when efflux, and (0.) when neither had the mastery. It will be 
observed that, beginning with exceptionally low water in April, 
1886, the surface reached a maximum height December, 1889, and 
that after an interval of ten years the minimum was regained in 
April, 1896. The record, therefore, covers a cycle of events, and 
comprises a fully rounded period. 



Table I. — Movement of Sublake in Hill Crest Well. 



Year. 


Jan. 


Feb. 


Mar. 


Apr. 
27" 


May. 
29" 


June. 
37" 


July. 
30" 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. ITotals. 


1886 




9 


-23" 


II 

-21 


-14 


-8" 


66 


1887 





-3 





33 


6 


5 


21 


8 


-19 


-10 


-22 


-19 





1888 


-3 


7 


26 


24 


18 


2 


-8 


-18 


-20 


-15 


-8 


-2 


3 


1889 


9 


1.2 


24 


12 


8 


9 


13 


7 


34 


16 


8 


15 


167 


1890 


-8 


-9 


-7 


10 


8 


-15 


-23 


-18 


-18 


-30 


-30 


9 


-131 


1891 


-21 


5 


31 


51 


33 


-6 


-28 


-24 


-20 


-13 


-17 


-12 


-21 


1892 


-5 


11 


10 


11 


11 


3 


-2 


-10 


-17 


-20 


-15 


-13 


-36 


1893 


-15 





9 


18 


26 


18 


4 


-16 


-20 


-21 


-12 


-9 


-18 


1894 


r 4 


-4 


7 


7 


13 


38 


41 


7 


-24 


-18 


-17 


-7 


39 


1895 








13 


10 


16 


10 


-6 


-14 


-21 


-19 


-20 


-14 


-45 


1896 


-12 


-9 


-3 




















-24 


Monthly 
averages, 


-5.9 


1.0 


lf.O 


20.'3 


16^8 


10" 1 


4/2 


-6.9 


-14.8 


-15.1 


-14.7 


-6.0 


Sums 
Equal 



The monthly averages give us the general trend of events. Com- 
mencing with the month of February we find the sublake rose 1 
inch. By the end of March it had risen 1 -4- 11 =12 inches. By 




O 










32 



10 



the end of April the elevation amounted to 1 + 11 + 20.3 = 32.3 
inches, and so on for the remainder of the year. Gathering these 
quantities, we have — 

Table II. — Average Eise of Hill Crest Sdblake. 



1886—1896. 


Jan. 


Feb. 


Mar. 


Apr. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Elevation of surface 


zero 


i'.'o 


12.0 


n 

32.3 


49.1 


59.2 


63.4 


56.5 


41.7 


26.6 


ii 
11.9 


5.9 



Since the table was built up from averages we must not expect 
it to emphasize special variations; for the grouping of averages 
resembles the grouping of pictures in composite photography. The 
combination invariably brings out class likenesses to the exclusion 
of individual features. Thus the table loses sight of an extraor- 
dinary year, like 1889 — full of plus quantities — also seasons of 
drought, like 1894 and 1895. It, however, clearly shows that influx 
has a tendency to prevail between February aud July, inclusive, 
and efflux to hold the mastery during the remaining months of the 
year. 

Experience proves that these limits are subject to variations, also 
that influx period usually lasts five months from the day it com- 
mences. Thus: 

When the influx begins in January it culminates in June. 
February " July. 

" " " March " August. 

April " September. 

It occasionally happens that the volume of influx exactly equals that 
of efflux. At such times the sublake remains statiouary ; thus : 

1892 — June 13 to July 23, Sublake immovable for 40 days. 
1893— February 4 to March 12, " " 36 " 

1895— January 1 to March 7, " " 65 " 

In all like cases the true turning-point is located midway in the 
stationary period. 

Close observation shows that a copious rainfall can make its 
journey to the sublake in twenty-five days, provided the soil has 
been saturated by frequent storms. But when the ground is moder- 



11 

ately dry it takes sixty days to cover the same distance. A period 
of drought prolongs the time to at least ninety days. Just in pro- 
portion, then, as the dryness of the soil increases will the time of 
descent be prolonged. 

For the present we shall accept as facts the following conditions, 
viz. : that the ratio of water volume at Hill Crest to the volume of 
rock holding the water is as 1 : QQ. That every inch in depth of 
the well holds 11.1 gallons. Also that the normal flow per square 
foot of water-bearing surface is 14.2 gallons in twenty-four hours. 
The proof will appear later on. 



Efflux. 

It has been found by experiment that efflux escapes over the 
border of the sublake very much like water escapes through a weir, 
and that for a given area of discharge the volume of flow is con- 
tracted to 60 per cent, of the normal, it therefore amounts to about 
8.6 gallons per square foot in twenty-four hours. 

Since every inch in depth of well holds 11.1 gallons, the depth 

equivalent to this flow will be =-^— . = 0.78 inch ; in other words : 

Daily Efflux = 0.78 inch, 
or 

E = 0.78 (expressed in depth of well). 

If we examine the records for 1890 and 1891 (when the ground 
was thoroughly moistened and the flow uniform) we find good 
illustrations of efflux extending over long periods. 

In 1890 sublake lowered 108 inches in 138 days (June 20 to Nov. 5), 
" 1891 " " 72 " " 92 " (June 20 to Sept. 20), 

Total, 180 inches in 230 days, 

which gives an average 

Daily fall of sublake = J ^ 

or 

E = 0.78 



12 

Showing complete accord between the data of calculation and those 
of experiment. This knowledge of the daily flow enables us to 
determine the yearly, which amounts to 

0.78 X 365 = 284.7 inches in rock depth. 

Since there are 66 cubic inches of porous rock around Hill Crest well 
to every cubic inch of water in suspension, the rock must contain as 
many inches of the annual rainfall as 66 is contained times in 284.7 
inches. Therefore 

Annual Efflux = 4.32 inches = 9 % rainfall. 
or 

Monthly Efflux = 0.38 of an inch. 

Experiment shows that annual fluctuations of the lake do not 
ultimately destroy the normal height • consequently efflux is an exact 
measure of that portion of the rainfall which, overcoming all hin- 
drances, arrives in safety at the sublake. 



Influx. 

Influx descends at every point over the surface of the sublake 
and at times greatly exceeds efflux, for the latter only takes place 
around the border. The total influx is always equal to efflux plus or 
minus a factor determined by observation. 

Since rainfall and efflux are expressed in inches of solid water, 
it is necessary to consider the water of influx distinct from the soil 
or rock into which it has flowed, and express it also in inches of 
solid water. This can be done for Hill Crest by dividing the rock 
depths by 66 ; the quotients will be the solid water equivalents. 
Calculating the same for Table I. we have : 



January 
February 
March 
April . 
May . 



5.9 diffused water = 6.09 solid water. 

1.0 " " = 0.015 " " 

11.0 " " = 0.167 " 

20.3 " " = 0.308 " 

16.8 " " = 0.254 " 



and so on. Expressing influx in tabular form we have 



13 



Table IIL— Total Influx. 



1886.-1896. MFEB.M.M.lTi 


W M ' Jl/iy M. SEP OCT 


M 


DEC 


TQTAl- 


MOHThU WR/)G&_°o 9 ws ./4 7 ,308 .* 


fy./S'/ .0btf-/0f?22't-ZV) 


-.223 


-.Of/ 


egv/ii. 


EFFLUX. .36 36 .36 .36 J 


6 .36 M .36 J6 .36 


.36 


.36 


K3Z 


TOTAL INFLUX o°.2j jpSz? £68 .6 


/</ ,f/</ yzy .2i's j 36 /«*/ 


J3J.26J 


¥*32 


M 








of, 
o.i 
OH 
03 
0.1 
0.1 




uW 








Hs 








' iKi 








i K. 




A 








ft 


'twtt 






1 III 1 1 




1 


PERCENTAGE. 6.2s 868 /no /£% a 


Ul /IfO 9.80 i'p 3./S 3.03 


3J] 


6.25 


/00°/o 



A moment's glance at these results shows that the least amount 
of water reaches the sublake during the month of October, and the 
greatest during April. These two months — separated by five inter- 
vening months of winter and five of summer — are characterized as 
months in which the average temperatures of atmosphere, earth, and 
sublake are practically equal (viz., 53° F.). As regards temperature, 
we should note, in passing, that in general terms : 



( The daily temperature ) 
I of ground water. i 



The average temperature of the j 



atmosphere throughout the year. 

From this general consideration of the questions of influx and 
efflux, we enter more particularly into that of distribution. 



Rainfall. 

The first step in our study of rain distribution is naturally a 
settlement of the question of monthly rainfall. 

Fortunately, the Annual Reports of the Philadelphia Water De- 
partment furnish complete data for the Neshaminy — a small stream 
which empties into the Delaware. This stream drains a water-shed 



14 

of 140 square miles. The country through which it passes resem- 
bles that around Bryn Mawr, and the annual rainfall is the same 
in both places. 

Collating said data, we have : 

Table IV. — Rainfall Averages. 



1886.- f 896. M FEB. MMM MAY JUN 


M M SEP OCT NOV. DEC TOTAL 


WIN FALL i/.0g 180 3J8 3.96 W5 MO 


SJ/ M] i/jS 3.5V 372 M 4fi/3 






if IV 


ilffw 


3fl|&l_u' ' Ti|| i|lfi'T 1 


fl x - *J-4 t ff~T s ftirtninHH||ft^"^ — — 


2 o|- _|_ - 


T T[ +T|f+ M|^ 




! 
i 

i-0 


1 " " " 




PERCENTAGE 8. \ 8. 8. / 70. f. 


//. ?. 8. 7. 8. 7. /00Z 



If we begin with the middle of April and divide the year into 
halves, we find : 

Rainfall of the summer half = 26.61 inches, 
winter " = 22.12 " 

Difference 4.49 inches, 

showing a difference of 20 per cent, more rain in summer than in 
winter. 

SlTKFACE-FLOW. 

The next question is : What amount of rainfall reaches the stream 
by passing directly over the surface of the ground ? In answer, we 
note first that the Neshaminy has been found to average as follows: 

Table V. — Stream-flow. 



1886—1896. 


Jan. 

3.54 


Feb. 
3'.22 


Mar. 


Apr. 


May. 


June. 


July. 


Aug 


Sept. 


Oct. 


Nov. 


Dec. 


Total. 


Stream-flow 


3".39 


2.18 


L89 


0"78 


1.13 


d'.98 


1.13 


0"99 


L78 


212 


2313 



15 

Whence it appears that the maximum amount of rainfall reaches the 
Neshaminy in January and the minimum in the month of June. 

The stream-flow, however, includes all those waters of efflux 
which the sublake is constantly pouring into the stream. If, now, 
we separate efflux from stream-flow we shall determine what amount 
passes over the surface of the ground. 

Table VI. — Surface-flow. 



/&86.-/8f6. JMFEB.fr 


m m. my m 


MY 


7/1/0. St 


r P OCT 


NOV. St 


'CWF/tL. 


ST/?£M FLOW. 3S</ 3.2Z 3 


3f 2/8 t'Sf 0J8 


7.73 


oft-/. 


''3 iff 


i.78 2. 


'fl 23 J 3 


EFFLUX. .36 .36 . 


36 .36 .36 .36 


.36 


M . 


36 .36 


.36 .. 


U 6/.3Z 


SURFFJCFFLOW 3./S Z.U J 


03 7.82 7.53 042 


O.JJ 


OM 


77 0.63 


7.1/2 7 U 


76 18.87 


3o jffTTW 












30 


Tff%i 


"% 










2 


zy -- 
1.0 


V 








if 


4 
10 




\ 


iflff 


11 mi 


\ 1 |1T 


fl 





Since the annual rainfall equals 48.73 inches, we have 

23 13 
Stream-flow = j^~o = 48 per cent, of rainfall. 

But we found efflux = 9 " 

Surface-flow = 39 per cent, of rainfall. 



Annual Flow. 

The average height of water in the ground for each month of the 
past ten years is found in Table II. and Fig. 2. These dimensions 
clearly indicate that (beginning with the month of February) the 
water steadily rises, as if a wave was in progress, and gains in 
volume each month until August, by which time it attains a height 
of 63.4 inches; after this it begins to subside, and finally reaches 
the old level in January. 



16 

Referring to Table III. we perceive that influx begins in October 
with 0.13 of an inch ; that it culminates in April with a height of 
0.67 of an inch, and subsequently drops back to its original level 
by the 1st of October. From which it appears that although the 
lake receives its maximum influx by the end of April, the wave 
attains its greatest elevation by the eud of July. Here, then, is a 
difference of three months ! 

To what is this great difference due? We answer, maiuly to the 
fact that efflux is constant and refuses to carry off (before the proper 
time) any excess that may be brought by influx. It follows that 
all such excess steadily accumulates. At last, when influx becomes 
less than efflux, subsidence ensues. 

"We can illustrate this rise and fall of the water by Fig. 4. Let 
£ C D F represent the section of a tank, having an outlet-pipe 

Fig. 4. 




at B which is left open all the time. The inlet-pipe A is of greater 
diameter than B. Turn on water and fill the tank to the level, C D. 
If now we graduate the flow at A so that influx and efflux are equal, 
the water-level will remain unchanged at C D. But if we open A 



17 



wider and admit a greater volume the surface, C D, will steadily rise 
to say E F. Now partly close A, so that efflux becomes greater 
than influx, and immediately the surface, E F, will recede toward 
C D, thus giving in miniature all of the eveuts of that wave-like 
flow which each year takes place at the sublake. If we represent 
the annual efflux by 100 per cent., we have for 

100 



One month, 



12 



8 A per cent. 



When, therefore, influx exceeds 8^ per cent, the lake will rise, and 
when it drops below 8^ per cent, the lake will fall. Subtracting this 
percentage of efflux from the percentages of influx, given in Table 
III., we find the percentage of accumulation for each month in the 
year 

Table VII. — Percentage of Accumulation. 



1886—1896 


Jan. 


Feb. 


Mar. 


April. 


May. 


Juue. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Total 


Influx 
Efflux 


6.25 
-8.33 


8.68 

-8.33 


12.20 

-8.34 


15.46 

-8.33 


14.21 

-8.33 


11.90 

-8.34 


9.80 
-8.33 


5.90 
-8.33 


3.15 

-8.34 


3.03 
-8.33 


3.17 
-8.33 


6.25 
-8.34 


+100 
-100 


Accumu- 
lation, 


-2.08 


035 


3.86 


7.13 


5.88 


3.56 


1.47 


-2.43 


-5.19 


-5 30 


-5.16 


-2.09 














Gathering the positive and negative percentages into separate col- 
umns, we have : 

Plus or Eising Percentage. Minus or Falling Percentage. 

August, 



February, + 0.35 



March, 

April, 

May, 

June, 

July, 



3.86 

7.13 = Max. 

5.88 

3.56 

1.47 



September, 

October, 

November, 

December, 

January, 



— 2.43 

— 5.19 

— 5.30 = Min. 

— 5.16 

— 2.09 

— 2.08 



Total, + 22 T 2 ^ fo 



Total, — 22^ fo 



Which proves that, beginning with February, the lake cannot help 
rising, because the influx accumulates steadily until August, after 
which time efflux gains the mastery and eventually works off the 
entire surplus. 



18 

It should be noted that the accumulation averages 22 t 2 7 5 q per cent, 
of the water that annually reaches the sublake, or 

0.2225 X 284.7 =■ 63.4 inches, 

the same maximum as given in Table II. and Fig. 2. We therefore 
regard the annual rise of water in the well as a natural sequence to 
accelerated influx coupled with constant efflux In like manner the 
annual fall is due to retarded influx coupled with constant efflux. 

On a grand scale this phenomenon finds its counterpart in the 
annual rise and fall of the waters of the great lakes. The outlets — 
the St. Mary, the St. Clair, and the Niagara Rivers — are relatively 
small. The average summer rainfall (as observed at Milwaukee, 
Wis., by the State Weather Service) exceeds the winter downpour 
by more than 40 per cent. This excess causes the surface of 

Lake Superior to rise 13 inches between March and September. 
Lake Michigan " 12 " " January and July. 

Lake Erie " 15 " " February and June. 

These elevations are based on measurements taken by the Engineer 
Corps of the United States Army [1860 to 1887], and show pre- 
cisely to what extent the restricted outlets bank up the water in the 
respective lakes. 

We also notice the working of the same principle during summer 
days. The hottest part does not occur at the noon hour — when the 
sun is on the meridian — but several hours later in the afternoon. 
In this case the accessions of heat arrive more rapidly than radiation 
is able to carry off. Radiation, however, keeps on apace, and, at last 
attaining the mastery, temperature falls. Ice-caves furnish still 
another example of the gradual procession in the seasons. 



Sublake Evaporation. 

Under the head of efflux we found that a constant quantity (0. 36 
of an inch of rainfall per month) passed away to the brook or stream 
quite independently of those (-f and — ) quantities that cause a rise 
or fall in the surface of the sublake. Let us now consider more 
closely the (+ and — ) quantities. In the first place, we see that 



19 

their sums are equal, because Table I. covers a cycle of time. 
Had either sum been in excess, the surface of the sublake would 
have stood accordingly higher or lower at the end of the period. 
Next we notice that the quantities have a minimum amount devel- 
oped in the month of October. Searching for the cause of this 
minimum we find it in the intense heat, great evaporation, and lux- 
uriant vegetation incident to the month of July, which parch the 
soil and develop evaporation over the surface of the sublake. The 
effect is cumulative, but maturity is reached after an interval of 
three months. Remembering that the maximum supply reached the 
lake in April and did not cease to manifest itself until after July, 
we conclude that in order to compare events happening at the sur- 
face of the sublake, with those at the surface of the ground, we 
must set our series of monthly averages (given in Table III.) back- 
ward three months and cause it to read thus : 



Table VIII. — Supply for Sublake Evaporation. 



1886—1896. 


Jan. 


Feb. 


Mar. 


Apr. 


May. 


June. 


July. 


Aug 


Sept. 


Oct. 


Nov. 


Dec. 


Total. 


Sublake: 
Increase 


.308 


.254 


.154 


.064 


-.105 


-.224 


-.229 


-.223 


-.091 


-.09 


.015 


.167 


+0.96 


Evaporation 




-0.96 









We see, then, that 0.96 of an inch is virtually set aside from the 
general supply to meet the requirements of evaporation which takes 
place at the sublake's surface, and that the increments composing 
this 2 per cent, of rainfall may be considered a sort of reserve fund 
from which the evaporations make draft without affecting the other 
quantities. Their balance, therefore, determines the rise or fall of 
the sublake. 

Let us now compare the results secured in Tables VI., III. and 
II., and determine the successive stages of rainflow. We discover 
at once that the ground receives or stores the greatest amount of 
water in the month of January (Table VI. ), that this supply reaches 
the sublake in April (Table III.), and that the effect of accumula- 
tion wears off by the end of July (Table II.). In view of this six- 



20 

months' period we conclude that the stages of rainflow are marked 
by very gradual progression, and observation proves that sudden 
storms at the surface of the ground do not indicate corresponding 
movements of the sublake. 



Surface Evaporation. 



We have at length reached a stage in our analysis where satisfac- 
tory data can be determined for the following subjects : 
1st. Monthly rainfall. 
2d. Surface-flow to the river. 
3c?. Efflux to the river. 
4th. Supply for sublake evaporation. 
If the data for subjects 2, 3, and 4 be added together and their 
sum subtracted from subject 1, the remainder will represent that 
part of the rainfall which is taken up by evaporation and vegeta- 
tion combined. Since vegetation withers in November and does 
not revive until April, we shall consider the months of December, 
January, February, and March by themselves, for in their case the 
differences will represent evaporation alone. 
Making the subtraction as indicated, we have : 

Table IX. 



1886—1896. 


Dec. 


Jan. 


Feb. 


March. 


Total. 


Evaporation 


6'. 953 


(X232 


o'.326 


o".236 


1.75 inches 



The excess in February is due to a mild interval that occurs in that 
month. During the remaining months of the year we have : 



Table X. 



1886—1896. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Total. 


Evaporation 
and Vegetation 


1.216 


3.'06 


3.42 


4.'l8 


3.'49 


3.'05 


2.'55 


L925 


22! 89 













21 



making a total in the twelve months of 24.64 inches. If this amount 
were deposited in an open reservoir, 85 per cent, would pass off 
by evaporation. It, however, falls on the earth, and for some time 
remains within reach of the sun's rays, its downward progress being 
impeded by grasses, leaves, mosses, roots, etc. In view of the small 
amount of water that ultimately reaches the lake, it is fair to assume 
that the total evaporation will not exceed one-half the open reser- 
voir amount — say 10.4 inches. But as 1.8 inches are evaporated 
from December to March, 8.6 will be evaporated from April to 
November. Subdividing and interpolating this quantity (having 
due regard to the character of the seasons) we obtain the following 
figures for evaporation : 

Table XI.— Surface Evaporation. 



1896. Jan. Feb. Mar. April. May. June. July. Aug. Sept. Oct. Nov. Dec. Total 



Surface Eva- 
poration 



0.2320.326 



0.236 



0.416 



0.86 



1.12 



1.38 139 



1.25 



1.15 



1.025 



0.953 



10.34 



Vegetation. 

The amount of water taken up by vegetation can now be deter- 
mined by subtracting the evaporation given in Table XI. (April 
to Nov.) from the joint supply of Table X. ; we have 

Table XII. 



1886—1896. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Total. 


Vegetation 


.8 


2.2 


2.3 


2.7 


2.2 


1.8 


1.4 


.9 


14.3 



We would add that the calorific effect of the seasons may be 
illustrated by the melting of ice under uniform conditions of ex- 
posure, as, for instance, ice that is kept in a refrigerator, thus : 



Yearly average. 


Jan. 


Feb. 


Mar. 


Apr. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Ice melted, lbs. 


300 


300 


400 


600 


750 


900 


1050 


1050 


900 


700 


600 


450 



22 



which shows a melting power in July 3| times as great as that in 
February. It will be seen that our distribution gives a ratio of 
about 3 to 1, which closely approximates the actual. 



Rainfall Distribution. 

We have now accomplished our purpose of supplying the missing 
chapter in the history of rainfall and traced its flow both over and 
within the surface of the earth. It only remains to gather all re- 
sults into one group so that relative proportions may become more 
apparent. 

Table XIII. — Rainflow. 



1886—1896. 


Jan. 


Feb. 


Mar. 


Apr. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Total. 


% 


Surface flow 


3.18 


2'.86 


3.03 


1.82 


1.53 


0.42 


„ ii 

0.77 1 0.62 


o'.77 


o".63 


l'.42 


1.76 


msi 


39 


" Evaporation 


.232 


.326 


.236 


.416 


.86 


1.12 


1.38 


1.39 


1.25 


1.15 


1.025 


.953 


10.34 


21 


Vegetation 








.8 


2.2 


2.3 


2.7 


2.2 


1.8 


1.14 


.9 




14.30 


29 


Sublake increase 


.308 


.254 


.154 


.064 














.015 


.167 






" Evaporation 










-.105 


-.224 


-.229 


-.223 


-.091 


-.09 






0.96 


2 


Efflux to River 


.36 


.36 


.36 


.36 


.36 


.36 


.36 


.36 


.36 


.36 


.36 


.36 


4.32 


9 


Monthly rainfall 


4.08 


3'.80 


3.78 


3.46 


4.95 


4.20 


5.21 


4.57 


4.18 


3.54 


3.72 


3'.24 


48.'73 


100 


Percentages 

Rainfall 


8 


8 


8 


7 


10 


9 


11 


9 


8 


7 


8 


7 


100 


% 



Omitting details, the final results may be summarized as follows : 

18.8 inches flow away over the surface of the ground = 39 % 

10.3 " pass off by evaporation . . . . = 21 

14.3 " are taken up by vegetation . . . = 29 

1.0 inch is evaporated from surface of sublake . = 2 

4.3 inches overflow from sublake to the river . . = 9 

Total 48.7 inches. 100 % 

A rainflow table can be constructed for any other locality by 
closely observing the principles enunciated in the foregoing pages 
and by gathering data in like manner. 



23 



LAWS OF RAINFLOW. 



Since our study of the phenomena of subterranean flow has been 
made principally in the light of data supplied by Hill Crest well, it 
is proper as introductory to the study of the laws of flow, first to 
inquire into the physical characteristics of that well. 

The curb is located 430 feet above sea-level and 80 feet above 
the nearest brook. The latter traverses a valley 1300 feet distant. 
The well was dug 6 feet in diameter to a depth of 65 feet through 
decomposed mica-schist, whose texture was sufficiently porous to 
admit the blade of a penknife. When first dug the water rose to a 
depth of 11 feet. The temperature of the water varied between 52° 
in winter and 54° in summer. Rock samples from this well were 
submitted to a skilled physicist, whose delicate experiments demon- 
strated the following facts : 

Weight of 1 cubic foot of perfectly dry rock . . . = 163.12 lbs. 
" 1 " " of water-soaked rock (drained) . = 174.675'' 
" 1 " " <•' " " (aotdrained) = 175.62 " 

These figures show that each cubic foot of dry rock requires 11.56 
pounds of water to fully moisten it, and when these demands are 
satisfied it further possesses a storage capacity of 0.945 pound of 
water subject to call. As one cubic foot of water weighs 62.3 
pounds, the interstices of the rock will approximate If per cent, of 
its volume, which gives us the constant relation of 1 volume of 
water to 65 volumes of rock, or 

-o _ 62.3 — 0.945 
0.945 
or 

R = 65. 

The well itself is lined with loose stones to within 10 feet of the 
top. The rest of the way the stones are laid in cement, and an extra 



24 

foot added to the wall. On it the curb was laid in a bed of cement, 
and the surrounding ground so filled in, rammed, and rounded as to 
make it utterly impossible for any surface-water to effect an entrance. 
A float was arranged in the well, with a suitable scale at the curb 
for indicating the depth of water. It may be objected that a 6-foot 
well is not an accurate unit of measure ; that but few wells are true 
cylinders ; that the diameter varies at different points ; also that the 
displacement due to the stone lining is an unknown quantity ! 
Granted that such irregularities do occur, but they only affect the 
sectional area of the well, and, whenever facilities exist for deter- 
mining its average water-section, they constitute no valid objection. 
The section can be ascertained by pumping, say, 500 gallons into a 
tank, recording how much the lake falls and the tank fills. The 
respective depths will be inversely as the sections, and we have : 

True water section = Section of 'tank X Rise in tank 

Fall of Lake. 

For Hill Crest the true water-section amounts to an area of 17.8 

square feet. Hence, 

Every inch in depth represents 111 gallons. 

Since the stone lining stands free of the earth's surface, the influx 
of water will not be impeded, and the entire circumference may be 
counted as effective water-bearing surface. Hence, 

Every inch in deptli will have 1.57 sq. ft. water-bearing; surface. 



Fading-Flow. 

The flow of water through a porous soil differs greatly from its 
passage through ordinary pipes. In the case of the latter the fric- 
tion is relatively small, but in the former it is very great. The soil 
not only resists the progress of the water at every point, but sustaius 
it so that head has no effect, and at the outlet the water escapes 
drop by drop from numberless pores. So slow is this process that 
each square foot of final area yields at Hill Crest only a few gallons 
every twenty-four hours. 

The best method to study flow is to pump the water from a well 



25 

and make record of the quantities and times of arrival during 
various stages of recovery. The intervals between readings must 
be regulated by the freedom with which the water returns. The 
data thus secured can be plotted as in Fig. 5, and the recovery line 
developed. Such a diagram will give the requisite material for calcu- 
lating flow from every square foot of exposed surface. When the 
water-level stands at G, the water in the ground will flow from the 
cylindrical surface, AG. The influx will cause the level to rise from 



Fig. 5. 



"'"'^'v"\ : ','';^- : 5 .SURFACE OF 







•~?Z ! #$ f. ;>3 * * 



G to H in a certain number of hours, and thereby reduce the area 
of the feeding surface from AG to AH. The mean depth of the 
feeding surface during the influx from G to H will equal AH + X 
X GH. In like manner the mean depth for a rise from H to J will 
equal A J -f- X X HJ } and so on for other volumes. 

In order to discover the values of the unknown factor X, we must 
carefully compare the volumes of flow which take place in two suc- 
cessive strata within equal lengths of time. Take, for instance, the 
strata G and H, as shown on the left-hand side of Fig. 5. In the 
first place we observe they represent two flows of entirely different 
character. The flow from G stratum is a fading flow, because the 



26 

outpour encroacnes on the flowing surface and diminishes its area 
until at length the surface, G, is entirely submerged. The flow from 
H stratum meantime is, on the contrary, a uniform flow, because its 
outpour falls into the cavity G and leaves the H flowing undis- 
turbed. 

We shall aim, therefore, to compare Jading flow with uniform flow 
and thus further our search for the unknown factor X. 

We learn from experiments recorded in Table XIV. that the 

Stratas J.H.G. furnished 633 gallons in 12 hours. 
J.H. " 366 " 12 '* 

Difference = 267 gallons. 

Or, more concisely, 

The flow from G = h + g = 1.00 
" " « H = h = .58 

Difference = 0.42 of G = g. 

In this stage of the inquiry it is important to note, that when the G 
flow finally fades away, the H flow then ceases to be a uniform one, 
and in turn becomes, like G, & fading flow, which submerges H in 
twelve hours. But this distance H is a counterpart of h in the 
flow G. It follows that g (the remainder) must have come from 
H itself while it was running as a uniform flow. 
In other words : 

f H stratum ) a 49 f J G stratum I 

I (with uniform flow). ) 1 (with fading flow), i 

Now G stratum by fading flow was covered in twelve hours. There- 
fore to cover the same surface by uniform flow would take as 

many times 12 as 0.42 is contained times in unity = ' ■ = 2.38, 

and 12 X 2.38 = 28.57 hours. , From which it is evident that 

uniform flow and fading flow are inversely as their times of flow. 

So that : 

G uniform : G fading : : 12 : 28.57 
and 

G uniform = " G fading 

2o.o7 

or 

G uniform = 0.42 G fading. 



27 

But G uniform is the same as flow from a mean area, and G fading 
the same as flow from a submerging surface. 
Hence, we have in general : 

Mean area of a submerging flow = 0.42 of the submerged surface. 

Consequently, 

X = 0.42 

So that 0.42 is the unknown factor, for which we have been search- 
ing. 

Applying same line of reasoning to other strata, we have : 

Water-bearing surface for HG = AH 4- 0.42 HG 
" JH = AJ + 0.44 JH 
" KJ = AK + 0.43 KJ and so on. 

Having thus determined the respective water-bearing surfaces, we 
finally divide each volume of recovery, GH, HJ, etc. (expressed in 
gallons), by the area of its water-bearing surface (expressed in square 
feet), and the quotients will measure the amount delivered by each 
square foot of water-bearing surface in the respective intervals of 
time. 

Experimental Results. 

A series of experiments was conducted at Hill Crest when the 
lake was in a state of repose. The pump was applied and 1468 
gallons of water removed, which lowered the level 132J inches, 
and furnished during recovery material for the following table: 

Experimental quantities are given in the first two columns. Ob- 
servations were made at twelve hour intervals and each successive 
rise of surface was measured by inches. Dimensions and quantities 
given in the remaining columns were determined by calculation 
according to principles already explained. A little later, when 
speaking of area of flow, we shall direct attention to the fact that, 
as recovery amounted to only 131 inches, it did not fully restore 
what pumping removed, but caused a shrinkage of 1J inches. 



28 



Table XIV. — Experiment of February, 1893. 



Recovery. 


Mean depths. 


Water- 
bear- 
ing 
sur- 
face. 


Yield per 
sq. ft. 


Percentage. 




Hours. 


Rise. 


Gallons. 


Values 
of X 


Depth 
of 

Free 
sur- 
face. 


Mean 
of 

fading 
sur- 
face. 


Total 
depth. 


12 hrs. 


24 hrs. 


Flow. 


Vor- 
tex. 


Vor- 
tex 
depres- 
sion. 


12 


57 


633 


0.42 


// 

74 


24" 


11 
98 


Sq. ft. 
154 


Gals. 
4.11 


Gals. 
8.2] 






11 
30 


12 


33 


366 


0.44 


41 


14 5 


55.5 


87 


4.2 


8.4 } 


60% 


40% 


16.4 


12 


18.5 


205 


0.43 


22.5 


8.0 


30.5 


48 


4.27 


8.6 J 






9 


12 


10.5 


117 


0.4 


12 


4.2 


16.2 


25.4 


4.6 


9.2 


65 


35 


4.2 


12 


6.5 


72 


0.45 


5.5 


2.9 


8.4 


13.2 


5.45 


10.9 


77 


23 


1.3 


12 


3.5 

2 


39 

22 


0.43 



2 



1.5 

1 


3.5 
1 


5.5 


7.1 


14.2 


100 

100 








12 






84 


131 


1454 




Average = 


23% 


of total. Mean 


=75 


% 



















Among other facts, we learn from the above that every square foot 
of Hill Crest rock has a normal flow of 14.2 gallons in twenty-four 
hours, also that complete recovery takes place in 84 hours. In 
addition to the above, like experiments were made in the months 
of January, February, March, June, July, September, and Decem- 
ber (but iu different years), and for quantities varying between 1000 
aud 3000 gallons. As the data so obtained included every variety 
of condition and fully confirmed the results of the foregoing series, 
we may safely rely upon the representative character of the figures 
given in the table. 

Vortex-flow. 



In the percentage column of Table XIV. we notice that the flow 
varied during the recovery period, the contraction reducing it to 60 
per cent, of the normal — the same as for water passing through a 
weir — and that more than ^ of the water returned on this basis. 



29 

After this the rate of flow expanded until finally the return entered 
at the normal rate, and by calculation the average for recovery was 
found to be 75 per cent, of the normal. 

This variation in flow is illustrated by Fig. 6. When the well 
was emptied from A to G, the water in the ground flowed from 
all directions horizontally toward the cavity AG, and formed a 
depression or vortex around the inlet to the well, which, of course, 
proportionally diminished the effective area of discharge. When 

Fig. 6. 



^"^"^.jt ^- T y y r ?fw.< ' a^^" cffrf>T-s» . 




the depth was AH = 74 inches, the vortex attained a depth of 30 
inches. As fast as the water flowed into the well the reduction in 
area was distributed between vortex and water-bearing surface. 
This equality of distribution lasted for thirty-six hours. Subse- 
quently the percentage of water-bearing surface increased and the 
vortex correspondingly diminished. Finally every square foot of 
water-bearing surface regained its normal yielding power, the vortex 
disappeared, and the water-level merged with the sublake level. 

We shall now state results of experiments made during the years 
1890-'93 and '97, so as to demonstrate what measure of harmony 



30 

existed under different conditions, with one standard porosity. In 
doing this, it will not be necessary to give every step with that 
minuteness which characterizes Table XIV., but only the salient 
points showing the true nature of the flow. By grouping the results, 
we obtain the following : 

Table XV. — Condensed Statement. 



Date of experiment. 


Gallons 
recovered . 


\% of entire 
Hours of j Recovery- 
recovery. : had a flow 
of 


Mean 
water- 
bearing 
surface. 


Mean flow. 


September, 1890 . 
February, 1893 . 
February, 1897 . 


2770 
1454 

822 


84 ! 60 pr.ct. 

84 j 60 " 
84 60 " 


23 pr.ct. 
23 " 
23 " 


75 pr.ct. 
75 " 
75 " 



We note that in every case complete recovery took place in 84 
hours ; although the amounts recovered varied between 800 and 
2800 gallons, the times did not vary. Also that about ^ of the 
entire recovery came with a constant flow of 60 per cent., leaving 
only |- for variable flow. Further, that the mean water-bearing 
surface was in each case 23 per cent, of the entire surface, and the 
mean flow was 75 per cent, of the maximum. 

Rock- and Water-sections. 



The experiments described under the head of fading flow prove 
that for any given ratio (between the solid rock-section and that of 
the interstices through which the water percolates) recovery always 
takes place in a fixed time, and the hours do not vary from this 
standard, no matter how great the volume. Thus 3000 gallons will 
return in identically the same time as 1000 gallons. We also saw 
under the head of efflux that a constant flow characterized a fixed 
ratio of rock- and water-sections, so that no matter how great the 
supply, the rate of efflux did not vary. From which we learn that 
every locality has a characteristic : 



31 

Fixed time of recovery 

and a 

constant rate of flow. 

For the purpose of establishing a formula expressive of the mutual 
relation existing between these conditions we shall adopt the fol- 
lowing : 

Notation. 

E = Max. daily efflux measured in inches of depth. 
EX 11.1= " " " " in gallons. 

" flow in gallons, from every sq. ft. of 
water-bearing surface. 
H = Total hours required for recovery. 
R = Number units rock-section to each unit of water. 
R -f- 1 = Rock- and water-sections combined. 

The value of E is determined by observations made on the descent 
of the sublake surface, as explained under the head of efflux. Divid- 
ing same by 24 we find the hourly descent. Taking one hour as 
our standard unit, we have : 

i — ^t- = depth of saturated rock. 
24 
■p 

— - = depth of water recovered ; 
24 l 

but these depths- are equal, 

. R+ 1 _ E 
24 24' 

It is, however, a fact that the flow producing the depth E does not 
cease when the height E has been reached, but will run for many 
hours before it spends itself, or all the interstices of the depth 

— ^tt — have emptied themselves, so as to restore the equilibrium. 
The total value is therefore equal to 



and we have the relation of 

R + 1 = E.H. 

or 

R = (ExH)-l. . . . (i) 



32 

The investigation of vortex-flow also furnished a means for ex- 
pressing the relation between the terms E and F. 
Thus: 

60 % F = E X 11.1. 
or 

F = 18.5 X E (2) 

Example : For Hill Crest the efflux E = 0.78, and the total hours 
required for recovery H = 84 ; substituting these values, we have : 

R = (0.78 X 84) — 1. 

Hence 

R = 65 = Number units rock-section to each unit of water. 



Sheinkage of Sublake. 

When the surrounding country is quite level and the sublake 
area of great extent, the removal of 1000 gallons by pumping will 
produce no more impression upon the sublake than would result 
from taking a bucket of water out of a pond. Such effect, however, 
would not be the case when the sublake underlies an undulating 
country, for the elevation of the ground naturally limits the lake 
area, so that a depression (say, one or more inches) would result 
from pumping out 1000 gallons. In the following investigation this 
depression will be spoken of as inches of shrinkage. 

To properly determine shrinkage involves a series of observations 
extending over a couple of weeks. 

With the sublake in repose, as in Fig. 7, each observation for the 
first four days will have one and the same reading. On the fifth 
day the pumping takes place, and in consequence the lake falls D 
inches. Recovery follows on the succeeding days, until at last the 
return ceases. The sublake surface will now be found at C, short 
of its former level AB by a distance S. The readings taken on the 
next five days will show that the shrinkage S is permanent. 

The second case of shrinkage is that where the sublake is steadily 
rising and should be plotted as shown in Fig. 8. Here the pump- 
ing interrupts the natural ascent of the water along the path AB. 



33 

The recovery ceases at the point C, a distance, ON, actually higher 
than the fifth-day reading, but falls short of the normal by a dis- 
tance S. 

The third case of shrinkage is developed when the sublake is 
steadily falling, and should be plotted as shown in Fig. 9. Here 
the total shrinkage seems equal to NC, but in reality BN is due 

Fig. 7. 




wholly to natural decline of the waters, while S is the shrinkage due 
to pumping. Whence we learn that the difference between readings 
(taken before and after recovery) only expresses true shrinkage when 
the lake is in repose. Also that this difference is of questionable 
magnitude when the sublake is steadily rising and excessive when the 
sublake is steadily falling. At times combinations of two cases occur 
and require careful consideration. 



34 



Velocity of Flow. 

A soil or disintegrated rock may have a uniform texture, but if 
it is traversed by water-bearing fissures they will develop a more 
rapid flow than the discharge due to texture per se. For this reason 
one may calculate the absorbent power of a rock specimen without 
in reality determining the resultant flow, as the latter depends on the 
presence or abseuce of fissures. The Hill Crest experiments give 
evidence that its flow was due alone to porosity of soil. The well, 
therefore, is a good one for the purpose of investigating the question 
of velocity. But whatever may be the final result, we should con- 
sider it more in the light of an approximation than an exact 
measurement. 

On general principles we have : 

C Original volume ^ ( Mean area of ] f Velocity ~\ ( Total \ 

X -j per hour > X \ hours of V 
in inches. ) I Recovery. J 



{Original volume ] r Mean area of ") 
occupied by >■ = < water-bearing > 
water and soil. J l surface in sq . in. J 



Notation. 

D = Depth in inches of Q gallons. 
H = Total hours required for recovery. 
E — Number of units of rock-section to each unit of water. 
R + 1 = Rock- and water-sections combined. 

Q = Number of gallons in a well of D depth. 

V = Average velocity- of horizontal flow in inches per hour. 

Embodying same in general formula, we have : 

231 Q (R + 1) = 144 (0.23 D X 1.57 X 0.75) X V X H . . ( 3 ) 
= 144 (0.27 D) V.H 
Since Q = 11 i 

V = 67JE + 1) 

11 

Example : In the case of Hill Crest R = 65 and H = 84. Sub- 
stituting the values of R and H in equation No. 4, we have : 

V = 52.6 inches per hour, 

which gives us the average velocity of flow in a horizontal direction 
during the time of recovery. 



35 

Area or Flow. 

When a large quantity of water has been removed from a well 
by pumping, the question arises as to what area of sublake will 
be disturbed by the process of recovery. In other words, how 
far-reaching is the influence of the vacancy caused by pumping? 
The answer is that in some cases the area can be determined ap- 
proximately, while in others it is practically unlimited, and those 
instances which show shrinkage at time of recovery are the only ones 
susceptible of calculation. 

The estimate for area of flow can be made on the general prin- 
ciple of cubic volumes of soil, viz.: 

i Total vol. of soil ] f That portion which } r That portion which] 
from which the r = "j supplies inflow > + < supplies inflow V 
water is drawn. ' *■ during pumping. • ( during recovery. J 

Notation. 

T = Total number of square feet in area of flow. 

S = " " of inches sublake is lowered by shrinkage. 

— = Portion of a day occupied in pumping. 



W = Influx (in gallons) during pumping. 

S 



Then : 

Total volume of soil from which the water is drawn = T X 



12 



That portion which supplies inflow during pumping = — —£j- — (R -f- 1) 

But 

{Mean area ^ ( Daily \ c Time 

laid bare I X 60 % \ max. flow V X } of 

by pumping. J ( per sq. ft. J I pumping. 

or 

W = i^£J> X 0.6 F X A 
2 24 

Introducing the value of F from equation 2, we have : 

W = 0.363 D.E.h (5) 

Substituting, we have : 

| That portion which 

(.supplies inflow during pumping=0.0486 D.E.h.(R-j-l). 



36 

And equation 2 expressed in cubic feet gives us : 

J That portion which 

I supplies inflow during recovery = 0.27 D _ H. 

After assembling the terms we find : 

5f = 0.0486 D.E.h. (K + 1) + 0.27 D. ^ H. 
12 \2i 



Therefore 



T =2[~0.27 V.H. + 0.58 E.h. (R + l).l . . (6) 



Example: In the case of the Hill Crest experiment of Feb. 1893, 

D = 132| E = 0.78 S = 1.25 

h=3 H = 84 V= 52.6 

R = 65 

Required the area of flow, from which the well gathered its water 
at time of recovery ? 

It is only necessary to substitute the above values in equation 6, 
to find : 

Area of flow = 135,680 square feet = 3Jjr Acres. 

Although this investigation shows that in cases of shrinkage it is 
quite possible to determine the acreage covered by the sublake, still 
its contour line can never be fixed, for that depends wholly on the 
characteristics of the soil or bed-rock. For a given locality it may 
be either a circle, an oblong, or any irregular figure. 



37 



POPULAR MISAPPREHENSION. 



It is a great mistake to imagine that rain- 
Slow Penetration fall penetrates rapidly to the lake. This is 
of Rainfall. rarely the case, and in many soils it takes 

months to accomplish the journey. In- 
stances have occurred at Hill Crest wherein the ground-water 
steadily lessened in months of heavy rainfall; also instances in 
which the water steadily rose in times of severe drought. 

For example, the surface of sublake lowered 52 inches during 
July and August, 1891, regardless of the fact that the rain fell in 
exceptionally large quantities, amounting to 10 inches. Again, the 
surface of the lake rose 42 inches between April 12 and May 3, 
1891, notwithstanding the fact that not a drop of rain fell, while the 
water was rising ! 

These facts show that no investigator is able to predicate the 
condition of ground-water from the data of a rainfall record, nor 
can he use the latter for the former under any circumstances. 

The theory of rainflow introduces a new 
Typhoid Fever view as to the healthfulness of ground- 
and Ground-Waters, waters, when considered in their relation 
to the increase or decrease of typhoid fever. 
For more than thirty years the German theory has found many 
advocates. The leading idea has been that a very close relationship 
exists between the annual rise and fall of ground-water and the 
increase or the decrease of typhoid fever. The ratio being an 
inverse one, viz. , as water subsides typhoid increases, as water rises 
typhoid diminishes. In our own country the subject has been care- 
fully investigated by the Board of Health of the State of Michigan. 
(See Annual Report for fiscal year 1894.) 

It is a notorious fact that many household wells are constructed 
with little regard to sanitary conditions. Some wells are exposed to 



38 

the air and sun, so that grasses and weeds grow during the summer 
months and fringe their border; while strong winds deposit dust 
and leaves over the surface of the water ; also various forms of 
animal life enter and die. Then, too, many wells are concave at 
the mouth, so that surface-water finds ready entrance during 
heavy storms. Worse still, many wells are sunk in porous soils in 
close proximity to cesspools or leaky drain-pipes. As all like con- 
ditions can be discovered and remedied, such wells form no part of 
our investigation, but must be ruled out of the question. Examin- 
ing the reports, we observe : First, that taking the health records 
given from 1889 to 1893 we are able to construct the following 
diagram : 

Table XVI. — Typhoid Reported its Michigan. 



/88f. -1893. 


JAN. 


FES. 


MM. 


m. 


MAY 


M 


MY MG. SEP. OCT W. DEC. 


PMCMTorTYPNOIk 


6. 


4 


3. 


3. 


3. 


S. 


6 /3. //. 22. // // 
















jflftlk 


/S - 














Ml 


if 














j\\ % " 


It' 














l' IrV 


o 








- 






J M 


7 














J\ 


a 














0v 


0' 








TTWF 


Ijf 


iff 


t::z :.: 



From which we learn that typhoid became alarming about the 
middle of August and attained its maximum virulence about the 
1st of November ; also that a small percentage existed during 
the first seven months in the year. Second. The annual rainfall 
in Michigan for the same period was about § the rainfall in 
Philadelphia. Third. The "representative well" in the Capitol 
grounds at Lansing had an annual oscillation similar to that shown 
in Table II., only the zero occurred in February, and the July 



39 

elevation averaged 13 inches, the extremes being 11 and 24. Surely 
this record does not favor the ground- water theory because typhoid 
reached its worse stage three months before the lowest water-mark 
was touched, and the epidemic completely disappeared by the time 
that mark was reached. According to such a showing, subsidence 
would be chargeable with causing an epidemic, both to rage and to 
abate. 

Let us now examine the data given in the same report for " many 
wells scattered throughout the Slate of Michigan" whose waters were 
carefully watched between 1878 and 1883. We see at once that the 
average soil was more porous than that around the Lansing well, 
for the greatest rise in any one year was 96 inches and the least 40. 
Constructing a table like No. II. we find : 

Table XVII.— Average Rise of Michigan Sublake. 




At first glance this table seems to favor the popular maxim : high 
ground-water, little typhoid; low ground- water, typhoid an epi- 
demic ! 

It must be remembered, however, that the process of averaging a 
six-years' record throws characteristic points into the shade and only 



40 

makes note of general features. For example, the 22 per cent, 
typhoid average came from a group whose extremes were 18 and 
37 ; in like manner the May 1st high-water-day, had for extremes 
April 1st and July 1st. Whenever, therefore, we aim to establish a 
true relation between two events occurring in a given year, manifestly 
we must not vitiate our data by diluting it with the diverse records 
of five other years. But, on the contrary, we should strengthen it 
by finding two consecutive years which have characteristic features 
as near alike as possible, and use them as a basis for comparison. 
Let us take 1879 and 1880, because in those years the epidemics were 
of equal virulence ; also the ground-water rose and fell almost equal 
distances. The most important events are given in the accompany- 
ing diagrams : 




The ground-water stood in each year at its highest level May 1st. 
Typhoid attained the alarming stage of 10 per cent, say, August 1st 
to 15th, and the maximum amounted to 25 per cent. Now note that 
the typhoid in one case became alarming sixteen days before low 
water, and in the other sixty days. The difference of forty-five days 
shows that the precise moment of low water had nothing to do 
with the origin of the disease. Also note that in 1880 typhoid 
reached its most virulent stage on the same day as low water, but in 



41 

1 879 it took ninety days after low water-mark was passed before it 
attained the same stage, showing that the precise moment of low water 
had nothing to do with the development of the disease. Incidentally 
the water rose in 1879, 20 inches. In harmony with the <l low- 
water theory " such a rise ought to have put a decided check upon 
the disease, but nothing of the kind occurred. It in fact had no 
influence whatsoever ! And why ? Simply because these phenomena 
were not related to each other as cause is to effect. The two diagrams 
flatly contradict each other. In 1879 the epidemic must be credited 
to 20 inches of rising water, while in 1880 an epidemic of equal 
violence raged with 20 inches of falling water. We might compare 
other years, but would find like inequalities and divergences. 

It is evident, therefore, that the Michigan data fail to establish 
any useful relation between the prevalence of typhoid and the height 
of the ground-water; whether we consider the data of the " represen- 
tative well " at Lansing, or whether we take the figures given for the 
u many wells throughout the entire State," the result is one and the 
same. 

According to the principles of rainflow, the lake is not a body of 
water that becomes more and more polluted as summer advances. 
Its surface is not lowered materially by evaporation ; it does not 
change in temperature, nor is it productive of either animal or vege- 
table life. On the contrary, its surface is lowered by natural over- 
flow; when fresh accessions arrive they come only through the 
superincumbent soil, so that every globule of the water is not only 
perfectly filtered, but in a rightly conditioned well it is both potable 
and healthful. 

These considerations convince us that the typhoid ground-water 
theory is not supported by facts ; also that whatever relation or 
synchronism does exist, it is merely a coincidence, and possesses no 
special significance. 

Many property-owners have an idea they 

Household Wells can secure a satisfactory well by digging far 

Should Never Fail, enough to find water; they then deepen the 

cavity, whatever may be necessary to hold 

the daily supply, and finally wall up the interior. The idea is an 

erroneous one and at variance with the principles of rainflow, for it 



42 

ignores the question of periodic fluctuations. The chances are that 
such a well will fail in times of great drought. 

Fortunately the remedy is always at hand, and tedious observa- 
tions are not necessary to solve the question. The right way is to- 
search the neighborhood for some Resident of twenty or thirty years' 
settlement, whose well has never failed, and learn from him the 
least depth of water his experience can recall. If perchance that 
depth would be sufficient for your daily wants, measure the present 
depth of water in his well, and dig your own well deep enough to 
secure precisely the same present depth. For example : If the resi- 
dent remembers one season in twenty years during which he had 
only 3 feet of water in his well, ask yourself the question : Would 
3 feet as a minimum satisfy my wants ? Afterwards measure his 
present supply. Suppose it amounts to 15 feet. Then dig your 
own well to whatever depth may be necessary to secure 15 feet of 
water. If, however, your wants exceed those of your neighbor, 
you should continue digging and deepen your own well enough to 
secure the excess also. Careful observance of this precaution is 
sure to give a never-failing supply. 



43 



RECAPITULATION. 



It has been shown that a very large part of the annual rainfall 
passes away over the surface of the ground. Hence the importance 
of using every means to preserve our forests. For wherever the 
country is thickly wooded the undergrowth, ferns, leaves, and mosses 
arrest the flow of water, to the great benefit of the land; freshets 
seldom occur, also protracted periods of drought and failure of 
springs are scarcely known. 

It has been demonstrated that the withdrawal of a thousand 
gallons from any well, located in a compact soil disturbs the sublake 
over many acres of ground. Therefore it is the part of wisdom 
always to anticipate the encroachments of a growing population by 
providing an independent water-supply, located far beyond the reach 
of contaminating influences. 

The study has served the good purpose of clearing away certain 
popular misapprehensions with regard to the relations between rain- 
fall and rainflow; between ground-water and typhoid fever; it has 
also suggested what precautions are necessary to insure a never- 
failing supply of health-giving water. 

Our investigation has taught us to recognize the world-wide exist- 
ence of the great subterranean lake, its characteristic features, its 
periodic fluctuations, and how to measure both volume and velocity 
of its unseen flow. The most striking features discovered are equa- 
tions Nos. 1 and 2 — showing the relation between rock- and water- 
sections ; also the analogy existing between the laws of subterranean 
flow and the laws governing the discharge of water through a weir ; 
the nature and process of recovery , likewise the relation between 
uniform flow and fading flow. Attention has also been directed to 
the fact that the daily temperature of ground water is equal to the 
yearly average temperature of the atmosphere. 

We believe that the present research has developed an outline of 
the genera] laws of rainflow, which for the first time places the sub- 
ject in its true light. 



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